Hello amisunshinee

You don't tell us what function you got for the volume, but I assume that you got:

$\displaystyle V = x(8-2x)^2$, where $\displaystyle x$ is the height of the box.

QUESTION:

I have done the data table and don't need help with that however these are the questions I'm stuck on.

5. Where does your function graph intersect the x-axis? These points are called the zeros of the function. Notice that you are able to see the zeros in the graph of the function but not in the graph of your actual data points. What is the reason for that? Think about the differences between real data and the graph of an equation.

I said that the graph intersects at (0,0) [Link to the graph I made:

http://i43.tinypic.com/2ir3v5j.png] but I don't understand how to explain the reason why and where I can go to find out about how to determine that.

Your graph is fine. But you'll see that there are two points where the graph meets the $\displaystyle x$-axis. The other one is $\displaystyle (4,0)$.

I think you're perhaps thinking that this is a harder question than it really is. The reason you can't see the zeros in the graph of your actual data is simply that you can't make a box that has either zero height ($\displaystyle x = 0$) or zero cross-sectional area ($\displaystyle x = 4$).

So in the graph of an equation, we may have values of $\displaystyle x$ that are not possible to obtain in practice.

2nd Question: What does the highest point of a cubic graph represent?

The highest point on the graph of your data (which occurs at approximately $\displaystyle x = 1.3$) represents the greatest volume that can be achieved using this size sheet of paper. That maximum volume is approximately $\displaystyle 38\text{ cm}^3$.

Grandad